Many conventional distributed ledgers, such as the blockchain used to support the Bitcoin cryptocurrency, are protected against attack by utilizing a large number of unknown “miners” to generate proof-of-work integrity checks. In such arrangements, the integrity check typically comprises a chain of hashes of all of the blocks of the distributed ledger. The integrity checks are therefore designed to be computationally very expensive to compute but very easy to verify. Moreover, there is generally no secret information utilized in computing the hashes of the blocks. This could lead to serious security problems if, for example, an attacker were able to aggregate more computational resources than the blockchain miner community. These and other issues also render conventional arrangements inappropriate for private blockchain implementations in which there are a relatively small number of known participants.